EDIT: ...ok, so both JaneBennet and Plato have different methods from mine, and theirs are similar, so chances are what I did was foolishness . you may ignore this post. i'll leave it up for anyone to comment on it.

EDIT: ...ok, so both JaneBennet and Plato have different methods from mine, and theirs are similar, so chances are what I did was foolishness . you may ignore this post. i'll leave it up for anyone to comment on it.

The posters proved this for any sets in general. You assumed it were finite sets and applied finite numbers.